Method and apparatus for producing three dimensional shapes

ABSTRACT

A method and system for automatically producing data representative of a modified head shape from data representative of a deformed head is provided. The method includes a step of processing captured data for the deformed head utilizing Principal Component Analysis (PCA) to generate PCA data representative of the deformed head. The method also includes the steps of providing the PCA data as input to a neural network; and utilizing the neural network to process the PCA data to provide data representative of a corresponding modified head shape.

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] The following related patent applications are being filed on evendate herewith and are assigned to a common assignee: Ser. No. __ /______, Cranial Remodeling Device Database by T. Littlefield and J. Pomatto;Ser. No. __/______ , Automatic Selection of Cranial Remodeling DeviceConfiguration by T. Littlefield and J. Pomatto; Ser. No. __/______,Automatic Selection of Cranial Remodeling Device Trim Lines by T.Littlefield and J. Pomatto; Ser. No. __/______ , Cranial RemodelingDevice Manufacturing System by T. Littlefield, and J. Pomatto. Thedisclosures of the above-identified applications are incorporatedherein.

FIELD OF THE INVENTION

[0002] This invention pertains to a system and method for producing datarepresentative of desired three dimensional shapes from correspondingdata representative of first three dimensional shapes, in general, andto a system and method for automatically producing data representativeof a modified three dimensional head shapes from corresponding datarepresentative of a deformed head shape.

BACKGROUND OF THE INVENTION

[0003] Cranial remodeling is utilized to correct for deformities in thehead shapes of infants. Prior to the development of the Dynamic OrthoticCranioplasty^(SM) method of cranial remodeling by Cranial Technologies,Inc, the assignee of the present invention, the only viable approach forcorrection of cranial deformities was surgical correction of the shapeof the cranium. Dynamic Orthotic Cranioplasty^(SM) utilizes a treatmentprogram in which a cranial remodeling band is custom produced for eachinfant to be treated. The band has an internal shape that produces thedesired shape of the infant's cranium.

[0004] In the past, the cranial remodeling band was produced by firstobtaining a full size and accurate model of the infants actual headshape. This first model or shape was then modified to produce a secondor desired head shape. The second or desired head shape is used to formthe cranial remodeling band for the infant. The first shape wasoriginally produced as a cast of the infant's head. The second shape wassimilarly produced as a cast of the head. In the past the second ordesired shape was obtained by manually modifying the first shape to formthe desired shape.

[0005] Various arrangements have been considered in the past to automatethe process of producing cranial remodeling devices. In some of theprior arrangements a scanner is utilized to obtain three dimensionaldata of an infant's head. Such arrangements have the disadvantage inthat scanners cannot obtain instantaneous capture of data of theentirety of an infant's head. In addition, it is proposed to utilizeexpert systems to operate on scanned data to produce an image of amodified head shape from which a cranial remodeling device may befabricated. However, because each head shape is unique, even the use ofan expert system may not present an optimized solution to developingmodified shapes suitable for producing a cranial remodeling device.

SUMMARY OF THE INVENTION

[0006] In accordance with the principles of the invention, a method forautomatically producing data representative of a desired head shape fromdata representative of a deformed head is provided. The method includesa step of processing captured data for the deformed head utilizingPrincipal Component Analysis (PCA) to generate PCA data representativeof the deformed head. The method also includes the steps of providingthe PCA data as input to a neural network; and utilizing the neuralnetwork to process the PCA data to provide data representative of acorresponding modified head shape.

[0007] In accordance with another aspect of the invention the methodincludes training the neural network to generate data representative ofdeformed shapes to corresponding modified shapes

[0008] In the illustrative embodiment of the invention the captured datacomprises first data points represented as Cartesian coordinates. Thefirst data points are utilized to produce second data representative oflengths of rays of predetermined orientation.

[0009] The number of second data points is chosen to be a predeterminednumber, n. An n x n covariance matrix is computed. Eigenvalues andeigenvectors are computed for the covariance matrix. The eigenvectorsfor a predetermined number of the largest eigenvalues are selected todefine PCA shapes as the PCA data. In the illustrative embodiment thepredetermined number of the largest eigenvalues is 64.

[0010] A system for automatically producing data representative of amodified head shape from data representative of a deformed head, inaccordance with the principles of the invention comprises one or moreprocessors operable to process captured data for a deformed headutilizing Principal Component Analysis (PCA) to generate PCA datarepresentative of the deformed head. The one or more processors arefurther operated to provide the PCA data as input to a neural network.The one or more processors are operated to utilize the neural network toprocess the PCA data to provide data representative of a correspondingmodified head shape.

[0011] In accordance with one aspect of the invention the one or moreprocessors operates to train the neural network to generate datarepresentative of modified shapes for corresponding deformed shapes.

[0012] In one embodiment of the invention a first database comprises afirst plurality of first sets of captured data, each first setcomprising captured data for a corresponding one first head shape. Asecond database comprises a second plurality of second sets of captureddata; each second set comprises captured data for a modified head shapefor a corresponding one of the first head shapes. A processor isoperable with a neural network program to train the neural networkprogram with the first plurality of first sets of captured data and thesecond plurality of second sets of captured data such that the neuralnetwork operates on a set of captured data for a first head shape toproduce a corresponding modified head shape.

[0013] In accordance with an aspect of the invention a support vectormachine program is operated to train the neural network program. In theillustrative embodiment of the invention the support vector machinecomprises a least squares support vector machine.

[0014] In accordance with other aspects of the invention, the method andapparatus produce data representative of a modified three dimensionalshape from data representative of a first three dimensional shape.

[0015] In accordance with another aspect of the invention, a databasefor use in generating PCA coefficients and for training a neural networkcomprises a first plurality of first sets of captured data, eachcomprising captured data for a corresponding one first head shape; and asecond plurality of second sets of captured data each comprisingcaptured data for a modified head shape for a corresponding one of saidfirst head shapes.

[0016] In accordance with another aspect of the invention each first setof captured data is obtained from a capture of a cast model of a firsthead shape. Each second set of captured data is obtained from a captureof a cast model of a corresponding modified head shape.

[0017] In accordance with another aspect of the invention the captureddata for each first set of captured data comprises a plurality ofCartesian coordinates each corresponding to a point on the correspondingone first head shape. The captured data for each second set of captureddata comprises a second plurality of Cartesian coordinates eachcorresponding to a point on a corresponding one modified head shape.

[0018] In accordance with another aspect of the invention, captured datafor each first set of captured data comprises a plurality of ray lengthsdefining the three dimensional shape of the corresponding first headshape. Captured data for each second set of captured data comprises aplurality of ray lengths defining the three dimensional shape of thecorresponding modified head shape.

[0019] In accordance with another aspect of the invention captured dataof each first set is converted from one coordinate system into datacomprising a plurality of ray lengths defining the three dimensionalshape.

BRIEF DESCRIPTION OF THE DRAWING

[0020] The invention will be better understood from a reading of thefollowing detailed description taken in conjunction with the drawingfigures in which like designations are utilized to identify likeelements, and in which:

[0021]FIG. 1 illustrates steps in a method in accordance with theprinciples of the invention:

[0022]FIG. 2 is a block diagram of a system in accordance with theprinciples of the invention;

[0023]FIG. 3 illustrates use of Principal Components Analysis and neuralnetworks in the illustrative embodiment of the invention;

[0024]FIG. 4 illustrates steps in accordance with another aspect of theinvention;

[0025]FIG. 5 is table;

[0026]FIG. 6 represents a neural network;

[0027]FIG. 7 is a graph; and

[0028]FIG. 8 is a block diagram of a system in accordance with theprinciples of the invention.

DETAILED DESCRIPTION

[0029] Turning to FIG. 1, steps 001 and 003 are steps that were utilizedin the past to produce a custom cranial remodeling device or band for aninfant with a deformed head. A positive life size cast is made of aninfant's head or a first shape as indicated at 001. A correspondingmodified cast or second shape is then made from which a cranialremodeling band is produced at step 003. In the past, a cranialremodeling band for the infant is produced by forming the band on thesecond cast which represents a modified head shape. A library ofhundreds of infant head casts and corresponding modified casts has beenmaintained at the assignee of the present invention and this library ofactual head casts and the corresponding modified casts is believed to bea unique resource. It is this unique resource that is utilized toprovide databases for developing the method and apparatus of the presentinvention.

[0030] An additional unique resource is that databases of additionalinformation corresponding to each infant have been developed by theassignee of the present invention. That database includes informationthat identifies the type of cranial remodeling device for each infanthead shape as well as the style of the cranial remodeling device andfeatures selected for incorporation into the cranial remodeling deviceto provide for appropriate suspension and correction of the deformity.Still further, each cranial remodeling device has trim lines that areuniquely cut so as to provide for appropriate suspension andfunctionality as well as appearance. A further database developed by theassignee of the present invention has trim line data for each-cranialremodeling device that has been previously fabricated corresponding tothe casts.. for unmodified heads.

[0031] In a first embodiment of the invention, shown as system 200 inFIG. 2, the databases 203, 205 of unmodified shapes and correspondingmodified shapes are used by a computer 201 to train a neural network300.

[0032] In accordance with one aspect of the invention, each unmodifiedor first head shape is digitally captured at step 005 as shown in FIG. 1by a digitizer 202 shown in FIG. 2, to produce first digital data atstep 007 to provide a complete three dimensional representation of theentirety of a head including the top portion. The first digital data isstored in database 203 at step 009. Each corresponding modified orsecond head shape is digitally captured by digitizer 202 at step 011 toproduce second digital data at step 013. The second digital data isstored in said database 205 at step 015. One to one correspondence isprovided between each first digital data and the corresponding seconddigital data as indicated at step 017. The correspondence betweendigital data for first and corresponding second head shapes ismaintained by utilizing any one of several known arrangements formaintaining correspondence.

[0033] In accordance with one aspect of the illustrative embodiment thefirst and second data stored comprises Cartesian coordinates for aplurality of points on the surface of the corresponding shape.

[0034] In the illustrative embodiment shown in FIG. 1, digitizer 202utilizes a plurality of digital cameras that are positioned tosubstantially surround the entirety of a cast or a patient's head suchthat a substantially instantaneous capture of the cast or of theinfant's head is obtained. As used herein, the term “digitizer” isutilized to identify any data capture system that produces digital datathat represents the entirety of a cast or a head and which is obtainedfrom a substantially instantaneous capture.

[0035] In accordance with an aspect of the illustrative embodiment ofthe invention, neural network 300 is “trained”, as explained below, sothat captured data of a first or unmodified shape 301 shown in FIG. 3which has no corresponding second or modified shape is processed byneural network 300 to produce a second or modified shape 303. Morespecifically, principal components analysis (PCA) is utilized inconjunction with neural network 300. Neural network 300 is trained byutilizing captured data for first shapes from database 203 withcorresponding captured data for second shapes from database 205.

[0036] Turning to FIG. 4, operation of system 200 is shown. At steps 401and 403, one or more databases are provided to store data for aplurality of first or unmodified captured shapes and to store data for aplurality of corresponding second or modified captured shapes.

[0037] The data from each captured first and second image is representedusing the same number of data points. In addition, all captured imagesare consistently aligned with each other.

[0038] The captured data for all head shapes represented in thedatabases 203, 205 of are aligned in a consistent way. The consistentalignment or image orientation has two separate aspects: alignment ofall captured modified images with each other as shown at step 405; andalignment of each unmodified captured image with the correspondingmodified captured image as shown at step 407. Alignment of unmodifiedand modified captured images ensures that the neural network willconsistently apply modifications. Alignment of the modified capturedimages with one another allows PCA to take advantage of the similaritiesbetween different cast shapes.

[0039] The casts from which the captured images are obtained do notinclude facial details. Typically the face portion is merely a plane.The position of the face plane is really a result of deformity. To alignthe shapes a manually iterative visualization process is utilized. Thisapproach “solved” half of the alignment issue - aligning all of themodified images with each other so that the principal componentsanalysis could take advantage of the similarities between these shapes.

[0040] To align each unmodified captured image with its correspondingcaptured modified image, alignment of the face planes is was utilized.For the most part, the face planes represent a portion of the shapesthat are not modified from the unmodified to the modified head shape andprovide consistency. An additional attraction to this approach is thatthere on the head actual casts, there is writing on the face planes andthis writing is visible in the texture photographs that can be overlaidonto the captured images. Alignment of face planes and writing providesa precise registration of the unmodified and modified captured images.

[0041] An automated approach to this alignment was developed usingseveral of the first captured images. The automated alignment workswhere texture photographs are well focused and clear. In other casesautomated alignment is supplemented with alignment by selecting“freehand” points on both the modified and unmodified images usingcommercially available software and then using the registration tool ofthat software. This approach aligned all unmodified captures withmodified captures so that corrections would be consistently applied.

[0042] The capture data for both the unmodified and modified head shapesare normalized at step 409 for training the neural network. As part ofthe normalization, a scale factor is stored for each for each normalizedhead or shape set.

[0043] As indicated at step 411, PCA is utilized with the aligned shapesto determine PCA coefficients. Because PCA uses the same set of basisvectors (shapes) to represent each head (only the coefficients in thesummation are changed), each captured image is represented using thesame number of data points. For computational efficiency, the number ofpoints should be as small as possible.

[0044] The original digitized data for first and second shapes stored indatabases 203, 205 represent each point on a surface using athree-dimensional Cartesian coordinate system. This approach requiresthree numbers per point; the x, y, and z distances relative to anorigin. In representing the head captures, we developed a scheme thatallows us to represent the same information using only one number perdata point. Mathematically the approach combines cylindrical andspherical coordinate systems. It should be noted that to obtain threedimensional representations of an object, a spherical coordinate systemmay be utilized. However, in the embodiment of the invention, the bottomof the shape is actually the neck of the infant, and is not of interest.

[0045] Conceptually this approach is similar to a novelty toy known as“a bed of nails.” Pressing a hand or face against a grid of moveablepins pushes the pins out to form a 3D copy on the other side of the toy.This approach can be thought of as a set of moveable pins protrudingfrom a central body that is shaped like a silo - a cylinder with ahemisphere capped to the top. The pins are fixed in their location,except that they can be drawn into or out of the central body. Usingthis approach, all that is needed to describe a shape is to give theamount that each pin is extended.

[0046] To adequately represent each head shape, a fixed number ofapproximately 5400 data points are utilized. To represent each of thecaptures using a fixed number of data points, the distance that each“pin” protrudes is computed. This is easily achieved mathematically bydetermining the point of intersection between a ray pointing along thepin direction and the polygons provided by data from the infraredimager. A set of such “pins” were selected as a reasonable compromisebetween accuracy of the representation and keeping the number of pointsto a minimum for efficiency in PCA. The specific set of points wascopied from one of the larger cast captures. This number was adequatefor a large head shape, so it would also suffice for smaller ones. Acommercially available program used to execute this “interpolation”algorithm requires as input the original but aligned capture data andprovides as output the set of approximately 5400 “pin lengths” thatrepresent the shape.

[0047] Using the consistent alignment and the consistent array of datapoints described above, the normalized data for each captured cast wasinterpolated onto this “standard grid.” Computing the covariance matrixproduced an n x n matrix, where “n” is the number of data points. As thename implies, this covariance matrix analyzes the statisticalcorrelations between all of the “pin lengths.” Computing the eigenvaluesand eigenvectors of this large covariance matrix provides PCA basisshapes. The PCA shapes are the eigenvectors associated with the largest64 eigenvalues of the covariance matrix. This approach of computingbasis shapes using the covariance matrix makes optimal use of thecorrelations between all the data points used on a standard grid.

[0048] PCA analysis allows cast shapes to be represented using only 64PCA coefficients. FIG. 5 sets out the hyper parameters for the 64 PCAcoefficients. To transform the unmodified cast shapes into correctmodified shapes, it is only necessary to modify the 64 PCA coefficients.For this processing task we selected and provide neural network 300 asindicated at step 413 of FIG. 4.

[0049] Neural networks are an example of computational tools known as“Learning Machines” and are able to learn any continuous mathematicalmapping.

[0050] As those skilled in the art will understand, learning machinessuch as neural networks are distinguished from expert systems, in whichprogrammers are utilized to program a system to perform the samebranching sequences of steps that a human expert would perform. Ineffect, an expert system is an attempt to clone the knowledge base of anexpert, whereas, a neural network is taught to “think” or operate basedupon results that an expert might produce from certain inputs.

[0051]FIG. 6 shows a conceptual diagram of a generic neural network 300.At a high level, there are three elements of a neural network: theinputs, á₁-á_(n), the hidden layer(s) 603, and the outputs β₁-β_(n). Aneural network 300 operates on inputs 601 using the hidden layer toproduce desired outputs 605. This is achieved through a process called“training.”

[0052] Neural network 300 is constructed of computational neurons eachconnected to others by numbers that simulate strengths of synapticconnections. These numbers are referred to as “weights.”

[0053] Training refers to modification of weights used in the neuralnetwork so that the desired processing task is “learned”. Training isachieved by using PCA coefficients for captured data representative ofunmodified casts of infant heads as inputs to the network 300 andmodifying weights of hidden layers until the output of the neuralnetwork matches PCA coefficients for the captured data representative ofcorresponding modified casts. Repeating this training thousands of timesover the entire set of data representing the unmodified andcorresponding captured shapes produces a neural network that achievesthe desired transformation as well as is statistically possible. In theillustrative embodiment, several hundred pairs of head casts wereutilized to train neural network 300 at step 415.

[0054] Testing on additional data from pairs of casts that the neuralnetwork was not trained with, or “verification testing”, was utilized inthe illustrative embodiment to ensure that the neural network 300 haslearned to produce the appropriate second shape from first shapecaptured data and has not simply “memorized” the training set. Once thistraining of neural network 300 is complete, as measured by the averageleast squares difference between the PCA coefficients produced by thenetwork and those from the modified cast shapes, the PCA coefficientweights are “frozen” and the network is simply a computer program likeany other computer program and may be loaded onto any appropriatecomputer.

[0055] A commercially available software toolbox was used to develop thelearning machine. The particular type of learning machine produced iscalled a Support Vector Machine (SVM), specifically a Least SquaresSupport Vector Machine (LS-SVM). Just like the neural networks describedabove, the SVM “learns” its processing task by modifying “weights”through a “training” process. But in addition to weights, the LS-SVMrequires a user to specify “hyper parameters.” For the radial basisfunction (RBF) type of LS-SVM used in this work, there are two hyperparameters: ã (gamma) and ó (sigma). The relative values of theseparameters control the smoothness and the accuracy of the processingtask. This concept is very similar to using different degree polynomialsin conventional curve fitting.

[0056]FIG. 7 shows a curve-fitting task in two dimensions for easyvisualization. Because there are a finite number of data points, (x,y)-pairs, it is always possible to achieve perfect accuracy by selectinga polynomial with a high enough degree. The polynomial will simply passthrough each of the data points and bend as it needs to in between thedata where its performance is not being measured. This approach providesridiculous results in between the data points and is not a desiredresult. One solution to this problem is to require that the curvedefined by the polynomial be smooth i.e., to not have sharp bends. Thissolution is fulfilled in the LS-SVM using a and 6. Higher values of ócorrespond to smoother curves and higher values of a produce greateraccuracy on the data set.

[0057] An unmodified or first shape represented by captured data isprocessed utilizing a principal components analysis algorithm. Theresulting PCA representation is processed by a neural network 300 toproduce a second or modified PCA representation of a modified shape.

[0058] In the system of the illustrative embodiment of the inventioncross-validation was used to choose the hyper-parameters. Data israndomly assigned to four groups. Three of the four groups were used totrain the LS-SVM, and the remaining set was used to measure theperformance in predicting the PCA coefficients for the modified headshapes. In turn, each of the four groups serves as the test set whilethe other three are used for training. The group assignment/division wasrepeated two times, so a total of eight training and test sets wereanalyzed (four groups with two repetitions). This process was repeatedfor a grid of (ã, ó)-pairs ranging from 0-200 on both variables. Therange was investigated using a 70×70 grid of (ã, ó)-pairs, so a total of4900 neural nets were tested for each of the first 38 PCA coefficients.From this computationally intensive assessment, hyper-parameters weredetermined and validated for the first 38 PCA coefficients andextrapolated those results to select hyper-parameters for the remaining26. Further “tuning” of the remaining 26 PCA hyper-parameters isunlikely to produce significant improvement in the final results becausethe first PCA coefficients are the most influential on the solution. Thetable shown in FIG. 5 presents the results for the hyper-parametertuning.

[0059] Once hyper parameters were tuned, the LS-SVM models generallyproduced errors of less than two percent for the PCA coefficients of themodified casts in test sets (during cross-validation). Applying thesetuned models to head casts that were not part of the cross-validation ortraining sets also generated excellent results.

[0060] There is a surprising variability of the head shapes asrepresented by cast shapes. Modified casts are not simply small changesto a consistent “helmet shape.” Each is uniquely adapted to theunmodified shape that it is intended to correct. Being so stronglycoupled to the unmodified shapes makes these modified casts surprisinglydifferent from one another. Of the several hundred casts that weanalyzed, each is unique.

[0061] Interpolating the aligned shapes also provided surprises andchallenges. The “bed of nails” concept is very effective in reducing thesize of the data sets and providing a consistent representation for PCA.It helps reduce the number of data sets that would have otherwise beenrequired to train a larger neural network. Instead of representing eachdata point by three components, each data point is represented by onecomponent thereby reducing the number of data sets significantly. Byutilizing this approach, the process is speeded up significantly.

[0062] Returning to FIG. 4, at step 415, neural network 300 is trainedas described above. Once neural network 300 is trained, it is thenutilized to operate on new unmodified heads or shapes to produce amodified or second shape as indicated at step 417.

[0063] Turning now to FIG. 8, a block diagram of a system 800 inaccordance with the principles of the invention is shown. System 800 isutilized to both train a neural network 300 described above and then toutilize the trained neural network 300 to provide usable modified headshapes from either casts of deformed head shapes or directly from suchan infant's head.

[0064] System 800 includes a computer 801 which may any one of a numberof commercially available computers. Computer 801 has a display 823 andan input device 825 to permit visualization of data and control ofoperation of system 800.

[0065] Direct head image capture is a desirable feature that is providedto eliminate the need to cast the children's head. An image capturingdigitizer 202 is provided that provides substantially instantaneousimage captures of head shapes. The digitized image 821 a is stored in amemory 821 by computer 801. Computer 801 utilizes a data conversionprogram 807 to normalize data, store the normalized data in memory 821and its scaling factor, and to convert the normalized, captured data to“bed of nails” data as described above. Computer 801 stores themodified, normalized data 821 b in memory 821. Computer 801 utilizing analignment program 809 to align modified data 821 b to an alignmentconsistent with the alignments described above and to store the aligneddata in an unmodified shapes database 803. Computer 801 obtains PCAcoefficients and weightings from a database 813 and utilizes neuralnetwork 300 and a support vector machine 817 to operate on the data fora first shape stored in memory 821 a to produce data for a modified orsecond shape that is then stored in memory 821 b. The data for themodified shape stored in memory 821 b may then be utilized to fabricatea cranial remodeling device or band for the corresponding head.

[0066] The invention has been described in terms of illustrativeembodiments. It will be apparent to those skilled in the art thatvarious changes and modifications can be made to the illustrativeembodiments without departing from the spirit or scope of the invention.It is intended that the invention include all such changes andmodifications. It is also intended that the invention not be limited tothe illustrative embodiments shown and described. It is intended thatthe invention be limited only by the claims appended hereto.

What is claimed is:
 1. A method for automatically producing datarepresentative of a modified head shape from first data representativeof a deformed head, comprising: processing said first data for saiddeformed head utilizing Principal Component Analysis (PCA) to generatePCA data representative of said deformed head; providing said PCA dataas input to a neural network; and utilizing said neural network toprocess said PCA data to provide second data representative of acorresponding modified head shape.
 2. A method in accordance with claim1, comprising: training said neural network to generate said second datafrom a database of first data and corresponding second data.
 3. A methodin accordance with claim 1, wherein: said first data comprises datarepresentative of lengths of rays of predetermined orientation.
 4. Amethod in accordance with claim 3, wherein: said second data comprises anumber of second data points chosen to be a predetermined number, n. 5.A method in accordance with claim 4, comprising computing an n x ncovariance matrix.
 6. A method in accordance with claim 5, comprising:computing eigenvalues and eigenvectors for said covariance matrix.
 7. Amethod in accordance with claim 6, comprising: utilizing eigenvectorsfor a predetermined number of the largest eigenvalues to define PCAshapes as said PCA data.
 8. A method in accordance with claim 7,comprising: selecting said predetermined number of the largesteigenvalues to efficiently represent each head shape.
 9. A method inaccordance with claim 8, wherein: said predetermined number of thelargest eigenvalues is
 64. 10. A method in accordance with claim 1,wherein: said first data comprises a predetermined number of first datapoints, the number of said first data points is chosen to be apredetermined number, n.
 11. A method in accordance with claim 10,comprising computing an n x n covariance matrix.
 12. A method inaccordance with claim 11, comprising: computing eigenvalues andeigenvectors for said covariance matrix.
 13. A method in accordance withclaim 12, comprising: utilizing eigenvectors for a predetermined numberof the largest eigenvalues to define PCA shapes as said PCA data.
 14. Amethod in accordance with claim 13, comprising: selecting saidpredetermined number of the largest eigenvalues to efficiently representeach head shape.
 15. A method in accordance with claim 13, wherein: saidpredetermined number of the largest eigenvalues is
 64. 16. A method forautomatically producing data representative of a modified head shapefrom data representative of a deformed head, comprising; providing afirst plurality of first sets of captured data, each said first setcomprising captured data for a corresponding one first head shape;providing a second plurality of second sets of captured data, each saidsecond set comprising captured data for a modified head shape for acorresponding one of said first head shapes; providing a neural network;training said neural network with said first plurality of first sets ofcaptured data and said second plurality of second sets of captured datasuch that said neural network operates on a set of captured data for afirst head shape to produce a corresponding modified head shape.
 17. Amethod in accordance with claim 16, comprising: utilizing PrincipalComponent Analysis to determine hyper-parameters for a predeterminednumber of PCA coefficients based upon said first plurality of sets ofcaptured data.
 18. A method in accordance with claim 16, comprising:selecting said predetermined number of PCA coefficients to be
 64. 19. Amethod for automatically producing data representative of a modifiedhead shape from data representative of a deformed head, comprising;providing a neural network trained with a first plurality of first setsof data, each said first set comprising captured data for acorresponding one first head shape, and with a second plurality ofsecond sets of captured data, each said second set comprising captureddata for a modified head shape for a corresponding one of said firsthead shapes; and utilizing said neural network to operate on datarepresentative of a deformed head to produce data representative of amodified head shape.
 20. A method for automatically producing datarepresentative of a modified head shape from data representative of adeformed head, comprising; providing a first plurality of first sets ofcaptured data, each said first set comprising captured data for acorresponding one first head shape cast; providing a second plurality ofsecond sets of captured data, each said second set comprising captureddata for a modified head shape cast for a corresponding one of saidfirst head shapes; providing a neural network; training said neuralnetwork with said first plurality of first sets of captured data andsaid second plurality of second sets of captured data such that saidneural network operates on a set of captured data for a first head shapeto produce a corresponding modified head shape.
 21. A method inaccordance with claim 20, comprising: utilizing a support vector machineto train said neural network.
 22. A method in accordance with claim 21,wherein: said support vector machine comprises least squares supportvector machine.
 23. A system for automatically producing datarepresentative of a modified head shape from data representative of adeformed head, comprising: one or more processors; said one or moreprocessors being operable to process data for said deformed headutilizing Principal Component Analysis (PCA) to generate PCA datarepresentative of said deformed head; said one or more processors beingoperated to provide said PCA data as input to a neural network; and saidone or more processors being operated to utilize said neural network toprocess said PCA data to provide data representative of a correspondingmodified head shape.
 24. A system in accordance with claim 23,comprising: said one or more processors being operable to train saidneural network to generate data representative of deformed shapes tocorresponding modified shapes.
 25. A system in accordance with claim 23,wherein: said captured data comprises first data points represented asCartesian coordinates; and said one or more processors operates toutilize said first data points to produce second data representative oflengths of rays of predetermined orientation.
 26. A system in accordancewith claim 25, wherein: the number of said second data points is apredetermined number, n.
 27. A system in accordance with claim 26,comprising said one or more processors operate to compute an n x ncovariance matrix.
 28. A system in accordance with claim 27, comprising:said one or more processors operate to compute eigenvalues andeigenvectors for said covariance matrix.
 29. A system in accordance withclaim 28, comprising: said one or more processors utilize eigenvectorsfor a predetermined number of eigenvalues to define PCA shapes as saidPCA data.
 30. A system in accordance with claim 29, comprising: said oneor more processors operates to select said predetermined number of thelargest eigenvalues to efficiently represent each head shape.
 31. Asystem in accordance with claim 30, wherein: said predetermined numberof the largest eigenvalues is no greater than
 64. 32. A system inaccordance with claim 23, wherein: said captured data comprises apredetermined number of data points, the number of said captured datapoints is chosen to be a predetermined number, n.
 33. A system inaccordance with claim 32, comprising said one or more processors operateto compute an n x n covariance matrix.
 34. A system in accordance withclaim 33, comprising: said one or more processors being operated tocompute eigenvalues and eigenvectors for said covariance matrix.
 35. Asystem in accordance with claim 34, comprising: said one or moreprocessors being operated to utilize eigenvectors for a predeterminednumber of the largest eigenvalues to define PCA shapes as said PCA data.36. A system in accordance with claim 35, comprising: said one or moreprocessors being operated to select said predetermined number of thelargest eigenvalues to efficiently represent each head shape.
 37. Asystem in accordance with claim 35, wherein: said predetermined numberof the largest eigenvalues is
 64. 38. A system for automaticallyproducing data representative of a modified head shape from datarepresentative of a deformed head, comprising; a first databasecomprising a first plurality of first sets of captured data, each saidfirst set comprising captured data for a corresponding one first headshape; a second database comprising a second plurality of second sets ofcaptured data, each said second set comprising captured data for amodified head shape for a corresponding one of said first head shapes;one or more processors programmed to operate on said first and saidsecond sets of data with a neural network; said one or more processorsbeing operated to train said neural network with said first plurality offirst sets of captured data and said second plurality of second sets ofcaptured data such that said neural network operates on a set ofcaptured data for a first head shape to produce a corresponding modifiedhead shape.
 39. A system in accordance with claim 38, comprising: aPrincipal Component Analysis program executable on said one or moreprocessors to determine hyper-parameters for a predetermined number ofPCA coefficients based upon said first plurality of sets of captureddata.
 40. A system in accordance with claim 39, comprising: saidpredetermined number of PCA coefficients is
 64. 41. A system forautomatically producing data representative of a modified head shapefrom data representative of a deformed head, comprising; a firstdatabase comprising a first plurality of first sets of data, each saidfirst set comprising data for a corresponding one first head shape; asecond database comprising a second plurality of second sets of data,each said second set comprising captured data for a modified head shapefor a corresponding one of said first head shapes; a neural networkprogram; a processor operable with said neural network program to trainsaid neural network program with said first plurality of first sets ofdata and said second plurality of second sets of data such that saidneural network operates on a set of data for a first head shape toproduce a corresponding modified head shape.
 42. A system in accordancewith claim 41, comprising: a support vector machine program operable totrain said neural network program.
 43. A system in accordance with claim42, wherein: said support vector machine comprises a least squaressupport vector machine.
 44. A method for automatically producing datarepresentative of a modified three dimensional shape from datarepresentative of a first three dimensional shape, comprising:processing data for said first three dimensional shape utilizingPrincipal Component Analysis (PCA) to generate PCA data representativeof said first three dimensional shape; providing said PCA data as inputto a neural network; and utilizing said neural network to process saidPCA data to provide data representative of a modified three dimensionalshape.
 45. A method in accordance with claim 44, comprising: trainingsaid neural network to generate data representative of correspondingmodified three dimensional shapes from said data for said first threedimensional shapes.
 46. A method in accordance with claim 44, wherein:said data of first three dimensional shapes comprises first data pointsrepresented as Cartesian coordinates; and said method further comprisesutilizing said first data points to produce second data representativeof lengths of rays of predetermined orientation.
 47. A method inaccordance with claim 46, wherein: the number of said second data pointsis chosen to be a predetermined number, n.
 48. A method in accordancewith claim 47, comprising computing an n x n covariance matrix.
 49. Amethod in accordance with claim 48, comprising: computing eigenvaluesand eigenvectors for said covariance matrix.
 50. A method in accordancewith claim 49, comprising: utilizing eigenvectors for a predeterminednumber of the largest eigenvalues to define PCA shapes as said PCA data.51. A method in accordance with claim 50, comprising: selecting saidpredetermined number of the largest eigenvalues to efficiently representeach shape.
 52. A method in accordance with claim 51, wherein: saidpredetermined number of the largest eigenvalues is
 64. 53. A method inaccordance with claim 44, wherein: said data of first three dimensionalshape comprises a predetermined number of data points, the number ofsaid data points is chosen to be a predetermined number, n.
 54. A methodin accordance with claim 53, comprising computing an n x n covariancematrix.
 55. A method in accordance with claim 54, comprising: computingeigenvalues and eigenvectors for said covariance matrix.
 56. A method inaccordance with claim 55, comprising: utilizing eigenvectors for apredetermined number of the largest eigenvalues to define PCA shapes assaid PCA data.
 57. A method in accordance with claim 56, comprising:selecting said predetermined number of the largest eigenvalues toefficiently represent each three dimensional shape.
 58. A method inaccordance with claim 56, wherein: said predetermined number of thelargest eigenvalues is
 64. 59. A method for automatically producing datarepresentative of a modified three dimensional shape from datarepresentative of a first three dimensional shape, comprising; providinga first plurality of first sets of captured data, each said first setcomprising captured data for a corresponding one first three dimensionalshape; providing a second plurality of second sets of captured data,each said second set comprising captured data for a modified threedimensional shape for a corresponding one of said first threedimensional shapes; providing a neural network; training said neuralnetwork with said first plurality of first sets of captured data andsaid second plurality of second sets of captured data such that saidneural network operates on a set of captured data for a first head shapeto produce a corresponding modified three dimensional shape.
 60. Amethod in accordance with claim 59, comprising: utilizing PrincipalComponent Analysis to determine hyper-parameters for a predeterminednumber of PCA coefficients based upon said first plurality of sets ofcaptured data.
 61. A method in accordance with claim 59, comprising:selecting said predetermined number of PCA coefficients to be
 64. 62. Amethod for automatically producing data representative of a modifiedthree dimensional shape from data representative of a first threedimensional shape, comprising; providing a neural network; utilizingsaid neural network to operate on a first set of data representative ofa first shape to produce a second set of data corresponding to amodified three dimensional head shape.
 63. A method in accordance withclaim 62, comprising; training said neural network with first pluralityof first sets of data and said second plurality of second sets of datasuch that said neural network operates on a set of captured data for athree dimensional shape to produce a corresponding modified threedimensional shape.
 64. A method in accordance with claim 63, comprising:utilizing a support vector machine to train said neural network.
 65. Amethod in accordance with claim 64, wherein: said support vector machinecomprises least squares support vector machine.
 66. A system forautomatically producing data representative of a modified threedimensional shape from data representative of a first three dimensionalshape, comprising: one or more processors; said one or more processorsbeing operable to process data for said first three dimensional shapeutilizing Principal Component Analysis (PCA) to generate PCA datarepresentative of said first three dimensional shape; said one or moreprocessors being operated to provide said PCA data as input to a neuralnetwork; and said one or more processors being operated to utilize saidneural network to process said PCA data to provide data representativeof a corresponding modified three dimensional shape.
 67. A system inaccordance with claim 66, comprising: said one or more processors beingoperable to train said neural network to generate data representative offirst three dimensional shapes to corresponding modified threedimensional shapes.
 68. A system in accordance with claim 66, wherein:said data for said first three dimensional shape comprises first datapoints represented as Cartesian coordinates; and said one or moreprocessors operates to utilize said first data points to produce seconddata representative of lengths of rays of predetermined orientation. 69.A system in accordance with claim 68, wherein: the number of said seconddata points is a predetermined number, n.
 70. A system in accordancewith claim 69, comprising said one or more processors operate to computean n x n covariance matrix.
 71. A system in accordance with claim 70,comprising: said one or more processors operate to compute eigenvaluesand eigenvectors for said covariance matrix.
 72. A system in accordancewith claim 71, comprising: said one or more processors utilizeeigenvectors for a predetermined number of the largest eigenvalues todefine PCA shapes as said PCA data.
 73. A system in accordance withclaim 72, comprising: said one or more processors operates to selectsaid predetermined number of the largest eigenvalues to efficientlyrepresent each three dimensional shape.
 74. A system in accordance withclaim 73, wherein: said predetermined number of the largest eigenvaluesis no greater than
 64. 75. A system in accordance with claim 66,wherein: said captured data comprises a predetermined number of datapoints, the number of said captured data points is chosen to be apredetermined number, n.
 76. A system in accordance with claim 75,comprising said one or more processors operate to compute an n x ncovariance matrix.
 77. A system in accordance with claim 76, comprising:said one or more processors being operated to compute eigenvalues andeigenvectors for said covariance matrix.
 78. A system in accordance withclaim 77, comprising: said one or more processors being operated toutilize eigenvectors for a predetermined number of the largesteigenvalues to define PCA shapes as said PCA data.
 79. A system inaccordance with claim 78, comprising: said one or more processors beingoperated to select said predetermined number of the largest eigenvaluesto efficiently represent each head shape.
 80. A system in accordancewith claim 78, wherein: said predetermined number of the largesteigenvalues is 64.